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Functional Inequalities for Particle Systems on Polish Spaces
Various Poincare-Sobolev type inequalities are studied for a
reaction-diffusion model of particle systems on Polish spaces. The systems we
consider consist of finite particles which are killed or produced at certain
rates, while particles in the system move on the Polish space interacting with
one another (i.e. diffusion). Thus, the corresponding Dirichlet form, which we
call reaction-diffusion Dirichlet form, consists of two parts: the diffusion
part induced by certain Markov processes on the product spaces
which determine the motion of particles, and the reaction part induced by a
-process on and a sequence of reference probability measures,
where the -process determines the variation of the number of particles and
the reference measures describe the locations of newly produced particles. We
prove that the validity of Poincare and weak Poincare inequalities are
essentially due to the pure reaction part, i.e. either of these inequalities
holds if and only if it holds for the pure reaction Dirichlet form, or
equivalently, for the corresponding -process. But under a mild condition,
stronger inequalities rely on both parts: the reaction-diffusion Dirichlet form
satisfies a super Poincare inequality (e.g. the log-Sobolev inequality) if and
only if so do both the corresponding -process and the diffusion part.
Explicit estimates of constants in the inequalities are derived. Finally, some
specific examples are presented to illustrate the main results.Comment: 22 pages, BiBoS-Preprint no. 04-08-153, to appear in Potential
Analysi
Dundee Discussion Papers in Economics 154:Labour demand in Germany: an assessment on non-wage labour
Dundee Discussion Papers in Economics 220:China's new labour contract law: no harm to employment?
In January 2008, China imposed a new labour contract law. This new law is the most significant reform to the law of employment relations in mainland China in more than a decade. The paper provides a theoretical framework on the inter-linkages between labour market regulation, option value and the choice and timing of employment. All in all, the paper demonstrates that the Labour Contract Law in it´s own right will have only small impacts upon employment in the fast-growing Chinese economy. On the contrary, induced increasing unit labour costs represent the real issue and may reduce employment
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